Geometric Formula as a Function problems
Perimeter as a Function of Area example question
a. Express the area, A , of an equilateral triangle as a function of one side S .
b. Express the perimeter, P , of the triangle as a function of the area A .
Solution to this Geometric Functions practice problem is given in the video below!
Asymptotes of Rational Functions problems
Vertical & Horizontal Asymptotes of a Function example question
Find the asymptotes, if any, in the following rational function:
Solution to this Asymptotes of Rational Functions practice problem is given in the video below!
Vertical & Horizontal Asymptotes of a Function example problem
Find the asymptotes, if any, in the given rational function:
Solution to this Asymptotes of Rational Functions practice problem is given in the video below!
Slant (Oblique) Asymptotes of a Function example
Find the asymptotes, if any, in the rational function below:
Solution to this Asymptotes of Rational Functions practice problem is given in the video below!
Rational Inequalities problems
Rational Inequalities example question
Find a solution set for the given rational inequality:
Solution to this Rational Inequality practice problem is given in the video below!
Quadratic Inequalities problems
Quadratic Inequality example question
Solve the given quadratic inequality:
Solution to this Quadratic Inequalities practice problem is given in the video below!
Absolute Value Equations problems
Double Absolute Value Equations example question
Solve the following absolute value equation:
Solution to this Absolute Value Equations practice problem is given in the video below!
Absolute Value Inequalities problems
Absolute Value Inequalities example question
Solve the following absolute value inequality and draw the solution set on a number line:
Solution to this Absolute Value Inequality practice problem is given in the video below!
Quadratic Functions problems
Quadratic Function Maximum Earnings example question
A tutor has 6 students per day when he charges $35 per hour for tutoring. For every increase of $5 in hourly rate, the daily number of his students decreases by 2. What are the maximum daily earnings possible?
Solution to this Quadratic Function practice problem is given in the video below!
Quadratic Functions Triangle Area Perimeter example problem
A right triangle has sides with lengths x, x + 7, and x + 8. Find the perimeter and area of the triangle.
Solution to this Quadratic Functions practice problem is given in the video below!
Linear Equations problems
Linear Equation: Percent Solution example question
A 6-gallon radiator is filled with a 40% solution of antifreeze in water. How much of the solution must be drained and replaced with pure antifreeze to obtain a 65% solution?
Solution to this Linear Equation practice problem is given in the video below!
Linear Equation: Upstream Downstream example problem
A crew of 8 can row 20 kilometers per hour in still water. The crew rows upstream then returns to its starting point in 15 minutes. If the river is flowing at rate 2 kilometers per hour, how far did the crew row?
Solution to this Linear Equation practice problem is given in the video below!
Linear Equation: Rate Time Distance example
At 1:30 p.m., Megan starts walking at a rate 4 miles per hour along a straight line path. Ten minutes later, Patrick starts walking in opposite direction at a rate 3 miles per hour along the same line path. If both carry a walkie-talkie whose maximum range is 0.9 miles, at what time will their connection be lost?
Solution to this Linear Equation practice problem is given in the video below!
Linear Equation: Youtube Views HARD example problem
A recipe video has 7,425 views and gets 590 views in 2 days, while a music video has 5,475 views and gets 495 views in 3 days. Assuming the rate of views for both videos was constant, how many days ago did these videos have the SAME number of views?
Solution to this Linear Equation practice problem is given in the video below!
System of Linear Equations: Elimination Method example
Solve the system of Linear Equations by Elimination:
Solution to this System of Linear Equations practice problem is given in the video below!
System of Linear Equations: Substitution Method example question
Solve the system of Linear Equations by Substitution:
Solution to this System of Linear Equations practice problem is given in the video below!
Logarithmic Word Problems
Natural Logarithm Word Problem example
If a beam of light that has intensity I is projected vertically downward into water, then its intensity I(x) at a depth of x meters is
At what depth is the intensity 
its value at the surface?
Solution to this Logarithms practice problem is given in the video below!
Common Logarithm Word Problem example question
The Beer-Lambert law states that the amount of light I that penetrates to a depth of x meters in an ocean is given by
a) Solve for x in terms of common logarithms
b) If c = 
, approximate the depth when 
. This determines the photic zone where photosynthesis can take place.
Solution to this Logarithms practice problem is given in the video below!
Common Logarithm Word Problem example problem
A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by
and that the drug to be effective, at least 2 milligrams must be in the body.
a) Determine the time when 2 milligrams are left in the body
b) What is the half-life of the drug?
Solution to this Logarithms practice problem is given in the video below!
Newton’s Law of Cooling example
Police arrive at a murder scene at 1:00 AM and immediately record the body’s temperature which was 92 degrees °F. At 3:00 AM, after thoroughly inspecting and fingerprinting the area, they again took the temperature of the body which had dropped to 87 degrees °F. The temperature of the crime scene has remained at a constant 71 degrees °F. Determine the time when the person was murdered. (Assume that the victim was healthy at the time of death. That is, assume that the temperature of the body at the time of death was 98.6 degrees °F).
Solution to this Law of Cooling Logarithms practice problem is given in the video below!
Logarithmic Equations problems
Solving Logarithmic Equations example question
Solve the following logarithmic equation and then check your solution:
Solution to this Logarithmic Equation practice problem is given in the video below!
Solving Logarithmic Equation example problem #2
Solve the given logarithmic equation and then check your solution:
Solution to this Logarithmic Equations practice problem is given in the video below!
Solving Logarithmic Equations example #3
Solve the logarithmic equation and then check your solution:
Solution to this Logarithmic Equation practice problem is given in the video below!
Solving Logarithmic Equation example question #4
Solve the given logarithmic equation and check your solution:
Solution to this Logarithmic Equations practice problem is given in the video below!
Solving Logarithmic Equations example problem #5
Solve the following logarithmic equation and check your solution:
Solution to this Logarithmic Equation practice problem is given in the video below!
Solving Logarithmic Equation example #6
Solve the following logarithmic equation and check the solution:
Solution to this Logarithmic Equations practice problem is given in the video below!
Solving Logarithmic Equations example question #7
Solve the logarithmic equation below and check your solution:
Solution to this Logarithmic Equation practice problem is given in the video below!
Expanding & Condensing Logarithms problems
Expanding Logarithmic Expression example question
Expand and simplify the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Expanding Logarithmic Expression example problem
Expand and simplify the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Condensing Logarithmic Expression example
Condense and simplify the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Condensing Logarithmic Expression example question
Condense and simplify the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Evaluating Logarithmic Expressions problems
Evaluating Logarithmic Expressions example question
Simplify and evaluate the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Evaluating Logarithmic Expressions example problem
Simplify and evaluate the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Evaluating Logarithmic Expressions example
Simplify and evaluate the following logarithmic expression:
Solution to this Logarithms practice problem is given in the video below!
Complex and Imaginary Numbers problems
Complex and Imaginary Numbers example question
1. Simplify the following complex number expressions:
a. 
b. 
2. Find the conjugate of the following complex number:
3. Evaluate the following complex number expression by using the appropriate complex number conjugate:
Solution to these Complex and Imaginary Numbers practice problems is given in the video below!
Radical problems
Radicals: Basic Properties example question
1. Determine whether the following expression is defined:
2. Show that the following identities hold:
a. 
b. 
Solution to these Radicals practice problems is given in the video below!
Radical-Exponent Conversion example problem
1. Convert the following expressions to Power or Exponent form:
a. 
b. 
c. 
2. Convert the following expressions to Root or Radical form:
a. 
b. 
Solution to these Radicals practice problems is given in the video below!
Radicals: Rationalizing Numerator & Denominator example
In the following expression, rationalize the numerator:
In the following expression, rationalize the denominator:
Solution to these Radicals practice problems is given in the video below!
HARD Square Root Algebra problem example question
Expression 
lies between which two whole numbers?
Solution to this Square Root Algebra practice problem is given in the video below!
Negative Exponents problems
Simplifying Expressions with Exponents example question
Simplify the following expression:
Solution to this Negative Exponents practice problem is given in the video below!
Negative Exponents: Factoring example problem
Factor the following expressions:
a. 
b. 
Solution to this Negative Exponents practice problem is given in the video below!
Scientific Notation problems
Exponents: Scientific Notation example question
1. Convert the following expression to exponential form and Scientific Notation:
a. 50,000
b. 821,423
c. 0.000324
d. 0.0000305
2. A particle travels at speed 0.06 ft/s. What is its speed in yd/s? Express the final answer in scientific notation.
Solution to these Exponents & Scientific Notation practice problems is given in the video below!
Exponents: Scientific Notation example problem
Convert the following expression to exponential form and Scientific Notation:
Solution to this Exponents & Scientific Notation practice problem is given in the video below!
Basic Exponents problems
Exponents: Basic Laws example question
Simplify the following using basic laws of Exponents:
a. 
b. 
c. 
d. 
e. 
f. 
Solution to this Exponents practice problem is given in the video below!
Rational Exponents: Basic Laws example problem
Determine whether the following expressions can be defined by using basic laws of Rational Exponents:
a. 
b. 
Solution to this Exponents practice problem is given in the video below!
Exponents: Natural Numbers example
Expand the following expressions into individual factors:
a. 
b. 
Solution to this Exponents practice problem is given in the video below!
Exponents: Negative Integers example question
Simplify the following expressions into fractions:
a. 
b. 
c. 
d. 
Solution to this Exponents practice problem is given in the video below!
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